Gaussian Process Regression with Mismatched Models

The behaviour is much richer than for the matched case, and could guide the choice of (student) priors in real-world applications of GP regression; RBF students, for example, run the risk of very slow logarithmic decay of the learning curve if the target (teacher) is less smooth than assumed. An important issue for future work-some of which is in progress-is to analyse to which extent hyperparameter tuning (e.g. via evidence maximization) can make GP learning robust against some forms of model mismatch, e.g. a misspecified functional form of the covariance function. One would like to know, for example, whether a data-dependent adjustment of the lengthscale of an RBF covariance function would be sufficient to avoid the logarithmically slow learning of rough target functions.